Theoretical Investigation on Structure-Property Relationship of Asymmetric Clusters (CH3FBN3)n (n = 1– 6)

Ma, Deng-Xue; Wei, Yao-Yao; Li, Yun-Zhi; Liu, Guo-Kui; Xia, Qi-Ying

doi:https://doi.org/10.1155/2020/4106562

Journal of Chemistry

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Abstract Introduction Results and Discussion Conclusions Data Availability Conflicts of Interest Authors’ Contributions Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2020 | Article ID 4106562 | https://doi.org/10.1155/2020/4106562

Theoretical Investigation on Structure-Property Relationship of Asymmetric Clusters (CH₃FBN₃)_n (n = 1– 6)

Deng-Xue Ma,¹Yao-Yao Wei,²Yun-Zhi Li,²Guo-Kui Liu,²and Qi-Ying Xia²

Academic Editor: Franck Rabilloud

Received02 Apr 2020

Revised15 May 2020

Accepted11 Jun 2020

Published30 Jun 2020

Abstract

The structural, relative stability, electronic, IR vibrational, and thermodynamic properties of asymmetric clusters (CH₃FBN₃)_n (n = 1–6) are systematically investigated using density functional theory (DFT) method. Results show that clusters (CH₃FBN₃)_n (n = 2–6) form a cyclic structure with a B atom and a N_α atom binding together. Five main characteristic regions are observed and assigned for the calculated IR spectra. The size-dependent second-order energy difference shows that clusters (CH₃FBN₃)₃ and (CH₃FBN₃)₅ have relatively higher stability and enhanced chemical inertness compared with the neighboring clusters. These two clusters may serve as the cluster-assembled materials. The variations of thermodynamic properties with temperature T or cluster size n are analyzed, respectively. Based on enthalpies in the range of 200–800 K, the formations of the most stable clusters (CH₃FBN₃)_n (n = 2–6) from monomer are thermodynamically favorable. These data are helpful to design and synthesize other asymmetric boron azides.

1. Introduction

The extensive studies on boron azides are developed as these molecules have been shown to be good precursors for boron nitride (BN) film deposition [1]. The chemistry of boron azides commenced in 1954 with the synthesis of boron triazide B(N₃)₃ [2]; since then, it developed slowly. In 1963, Paetzold produced trimeric (Cl₂BN₃)₃ from the reaction of LiN₃ and BCl₃ in CH₂Cl₂ solution [3]. The molecular structure of dichloroboron azide containing six-membered boron nitrogen heterocycle with diazo groups bounded to nitrogen atoms was determined by Müller in 1971 [4]. Boron dihalide azides (BX₂N₃)₃ (X = F, Cl, or Br) from the reaction of BCl₃ with trimethylsilyl azide in CH₂Cl₂ solution were also recorded by Wiberg et al. in 1972 [5]. Dehnicke reported the infrared spectra of the monoazide products, I₂MN₃ (M = B, Al, Ga), and observed the formation of oligomers of these species in 1978 [6]. Several alkyl and arylboron azides have been synthesized using similar methods. Oligomerization for Me₂BN₃ was established by ¹¹B NMR spectroscopy in 1966 [7]. The chemistry of alkylboron azides was further investigated, and the development of this field has been reviewed by Paetzold, Fraenk, and coworkers [8–16].

Although the chemistry of boron azides in the condensed phase has been extensively discussed in the literature, research studies of these species in the gas phase are rather limited. With the goal to use boron azides as the single-source precursors (SSP), knowledge of their gas phase stability and thermodynamic properties becomes essential. The structure of monomers Cl₂BN₃ and (CH₃)₂BN₃ has been explored using ab initio calculation, and the thermodynamic stabilities of X₂BN₃ with respect to its dimerization and trimerization have been gained and discussed [17–20] from the theoretical view. Previous theoretical studies of the boron azides mostly focused on the symmetric boron azides.

The effect for the break of the symmetry of substituted boron azides is hardly considered. Here, in accordance with previous theoretical studies on the asymmetric clusters of inorganic boron azides [21, 22], and experimental studies on the asymmetric clusters of organic gallane azides and aluminum azides (RR’MN₃)_n (M = Al, Ga; R = CH₃; R’ = H, Cl, Br; n = 3−4) [23, 24], the structure, stability, IR spectra, and thermodynamic characteristics of the asymmetric clusters of organic boron azides (CH₃FBN₃)_n (n = 1 – 6) were theoretically discussed in detail. These discussions will provide fundamental data and references for experimentalist to design and synthesize the novel boron azides in the future.

2. Computational Methods

As is well known, it is important to choose an appropriate basis set to give the accurate description of clusters’ structures and energies. Usually, a substantial size of basis set is required. However, the size of clusters studied in this work excluded the use of a very large basis set, and hence, all calculations were performed using the DFT-B3LYP method with the 6-31G basis set [25, 26] via the Gaussian 09 program package with the default convergence thresholds [27]. To ensure the adequacy of this basis set, we also optimized the clusters with the 6-311 + G basis set. As shown later on, results obtained from these two basis sets were similar except for slightly numerical differences. The energies of all clusters were also evaluated using the 6-311 + G basis set. The initial configurations are searched by two ways: (1) by considering the numbers of known clusters (HClBN₃)_n (n = 1–6) in previous works [21] and (2) by placing -CH₃ groups and F atoms at various substitutional sites (H or Cl) on the basis of optimized (HClBN₃) geometries. No symmetry constraints were applied. Lots of rationally initial one-, two-, and three-dimensional configurations were built to seek the most stable structures. In this way, a large number of optimized isomers for the asymmetric clusters (CH₃FBN₃)_n (n = 1–6) were obtained. Frequencies as well as their respective IR intensities were then calculated, and the lack of imaginary frequencies confirmed that the true minimum was obtained in each case. According to the previous study, the calculated frequencies were scaled uniformly by 0.96 to approximately correct the systematic overestimation [28].

3. Results and Discussion

3.1. Structures and Charge Distribution

A number of isomers are calculated at each size. Here, structures of clusters (CH₃FBN₃)_n (n = 1 − 6) having the lowest energy were focused because all properties of clusters (CH₃FBN₃)_n (n = 1–6) were calculated based on the lowest energy. Two stable structures of the monomer CH₃FBN₃ were obtained (connectivity: CH₃FB−N_α−N_β−N_γ) with a slight difference in geometrical parameters. The clusters (CH₃FBN₃)_n (n = 2 – 6) are produced by the head-to-tail oligomerization of the CH₃FBN₃ monomers, which is a starting point for the oligomerizations. Two dimers, seventeen trimers, sixty-four tetramers, two hundred and fifty-six pentamers, and five hundred and thirty-six hexamers are obtained in this manner. Judged by the total energies, the most stable isomers at each size are labeled as 1, 2, 3, 4, 5, and 6 and shown in Figure 1. Obviously, B and N_α atoms easily bond together, and B–B and N_α–N_α bonds are not formed in the clusters (CH₃FBN₃)_n (n = 2 − 6). In other words, the clusters (CH₃FBN₃)_n (n = 2 − 6) contain cyclic (BN_α)_2n structures with alternating boron and α-nitrogen atoms.

The corresponding geometrical parameters are collected in Table 1, and the data in parentheses are calculated results from the 6-311 + G basis set. The results obtained from different basis sets are generally consistent. In detail, bond lengths (except for B−F bonds) from the 6-311 + G basis set are slightly shorter than those from the 6-31G basis set. This whole agreement shows that it is appropriate to choose the 6-31G basis set to compute the titled systems. Therefore, in this work, we only report the geometrical parameters obtained with the 6-31G basis set. For n = 1, the azide group in the monomer CH₃FBN₃ is slightly bent with a N_α–N_β–N_γ angle of 173.1°. The calculated B–N bond length of 1.447 Å is between B–N single (1.58 Å) and double bonds (1.37 Å). The N_β−N_γ bond length at 1.135 Å is shorter than the N_α−N_β bond length at 1.240 Å. The N_β−N_γ bond length is between N–N double (1.25 Å) and N–N triple bonds (1.10 Å). For n = 2 – 6, the computed B–N bond length of 1.601–1.638 Å possesses typical character of B–N single bond, which is similar to the B–N length of other covalent boron azides previously determined, such as (F₂BN₃)₃ (1.616 Å) [19] and (C₆F₅B(N₃)₂)₃ (1.60 Å) [12]. The B−C and B−F bond lengths are in the range of 1.585–1.596 Å and 1.363–1.381 Å, respectively. The computed structural parameters of the azide units in the clusters (CH₃FBN₃)_n (n = 2 – 6) are 1.240–1.255 Å for N_α−N_β bonds, 1.128–1.133 Å for N_β−N_γ bonds, and 177.1–179.4° for N_α−N_β−N_γ bond angle. It is obvious that the azide group is nearly linear. These results are perfectly consistent with those found in (Cl₂BN₃)₃ (1.25 Å, 1.09 Å, 178°) [4], (F₂BN₃)₃ (1.249 Å, 1.129 Å, 179.8°) [19], and (C₆F₅B(N₃)₂)₃ (1.27 Å, 1.11 Å, 179°) [12]. Therefore, the calculation method in this work is reliable, and it gives credence to our computed structural parameters of clusters (CH₃FBN₃)_n (n = 2 – 6).

Through the above discussions, it is obvious that N_β−N_γ bond is shorter than N_α−N_β bond in the clusters (CH₃FBN₃)_n (n = 1 – 6). This can be interpreted as a higher bond order for the terminal N−N bond, showing a preformation of the N₂ molecule. Moreover, the cluster size n has an important effect on the geometries. An obvious increase is shown for the length of B-N_α bond with cluster size n increasing from 1 to 2∼6 owing to the tension of the ring. However, B−N_α bond length shows little change with cluster size in the range of 2∼6, which fluctuates in the range of 1.601–1.638 Å. The N_α−N_β bond lengths increase as the cluster size n increases from 1 to 5 and show little change from n = 5 to n = 6. Similarly, when cluster size n increases from 1 to 3, the B−C and B−F bond lengths increase. However, the change of B−C and B−F bond lengths is not obvious from n = 4 to n = 6. The N_β−N_γ bond length shortens from 1.135 Å in cluster size with 1 to 1.129 Å in cluster size with 6 and tends to be constant around 1.130 Å with n = 3 – 6. Compared with monomer 1, the increasing bond lengths of N_α−N_β, B−C and B−F bonds that are outside of rings show that N₂ (N_β−N_γ), -CH₃, and F^- groups can be easily removed to yield BN material.

To give a deeper understanding on these structures, we calculate the charge distribution of the clusters (CH₃FBN₃)_n (n = 1 – 6) as shown in Table 2. It can be seen that the charge distribution of CH₃FBN₃ molecule exhibits zwitterionic characteristics with the charge centers of N and B atoms, respectively. As for (CH₃FBN₃)_n (n = 2 – 6), charge distributions are similar to those of CH₃FBN_3. However, because B atoms in these molecules all reach the high coordination, the characteristic of zwitterionic ion for these clusters is a problem needing more studies.

3.2. Relative Stabilities

All energies are displayed in Table 3, and the data in parentheses are from the 6-311 + G basis set. Obviously, the energies obtained at the B3LYP/6-31G levels are similar to those obtained with the 6-311 + G basis set. The use of larger basis sets has no significant influence on the binding energies, which again shows that the 6-31G basis set is suitable for the clusters studied here. Thus, in this work, we only report the relative stability of the clusters (CH₃FBN₃)_n with the 6-31G basis set. The uncorrected binding energies (E_b), corrected binding energies (E_b-c), average corrected binding energy (E_b-c-ave), and the second-order energy difference (Δ₂E) are calculated using the following equations:where E (CH₃FBN₃)_n and E (CH₃FBN₃) are the total energies of the clusters (CH₃FBN₃)_n (n = 2 – 6) and CH₃FBN₃, respectively; ZPE (CH₃FBN₃)_n and ZPE (CH₃FBN₃) represent the zero point energies of the most stable clusters (CH₃FBN₃)_n (n = 2 – 6) and CH₃FBN₃, respectively; and the 0.96 is a scaling factor [28].

From Table 3, the ratios of ZPE corrections to their binding energies E_b are large for the clusters (CH₃FBN₃)_n (n = 2 − 6). Thus, it is necessary to carry out the ZPE corrections for the binding energies. For intuitive presentation, the calculated energy is also plotted as a function of cluster size n as shown in Figure 2. The curves of E_b (Figure 2(a)) and E_b-c (Figure 2(b)) are seen to increase monotonically with the augment of cluster size n, which means that clusters can continue to gain energy during the clusters’ growth process. The E_b-c-ave values increase sharply with the clusters size n from 2 to 3; then, it approaches to be stable around 13–14 kJ·mol⁻¹ when cluster size n ≥ 3. Therefore, the geometrical structures of clusters (CH₃FBN₃)_n (n = 1 − 6) tend to be stable when cluster size n ≥ 3.

The relative stability of clusters can be also estimated through the Δ₂E (n). According to the definition, clusters with positive Δ₂E are more stable than those with negative Δ₂E. A clear odd-even oscillation behavior is presented in Figure 2(d). The clusters (CH₃FBN₃)_n (n = 1 − 6) at n = 3, 5 correspond to local maximal on the curve of Δ₂E, indicating that they are relatively more stable than other clusters. This trend is in excellent agreement with that of the asymmetric clusters of the inorganic boron azides (HClBN₃)_n (n = 1 – 6) [21]. In particular, the trimer (CH₃FBN₃)₃ possesses the highest stability among all clusters in terms of the largest value of Δ₂E. The stable structure of six-member ring of trimer plays a vital role.

3.3. IR Spectrum

The IR spectrum is not only the basic property of compounds and effective method to analyze or identify substances, but also has a direct relationship with thermodynamic properties. However, there are no experimental data for the title compounds. Thus, it is necessary to use the theoretical method to calculate and predict IR spectra for both theoretical and practical reasons. Figure 3 provides the calculated IR spectra of the clusters (CH₃FBN₃)_n (n = 1 − 6) at the B3LYP/6-31G level. Due to intrinsic complexity, it is difficult to assign all vibrational modes. Thus, we only analyze and discuss some typical vibrational modes.

There are five main characteristic regions for clusters (CH₃FBN₃)_n (n = 1 – 6) that correspond to the –N₃ asymmetric and symmetric stretching, –CH₃ stretching and in-plane bending vibrations, and the fingerprint region. As for monomer CH₃FBN₃, the –N₃ asymmetric and symmetric stretching vibrations with intense peak lie at 2215 and 1360 cm⁻¹, respectively. The modes in the range of 2923–3022 cm⁻¹ are classified to the characteristic –CH₃ stretching vibrations. The peak around 1440 cm⁻¹ corresponds to the –CH₃ in-plane bending vibrations. The peaks at less than 1210 cm⁻¹ belong to the fingerprint region, which are mainly composed of wagging and scissoring of –CH₃ and the stretching of B−F and B−C bonds. As can be seen from Figure 3, similar vibrational modes are observed in clusters (CH₃FBN₃)_n (n = 2 – 6). The regions of 2917–3019, 2202–2243, 1331–1458, 1217–1308, and 0–1204 cm⁻¹ are individually assigned to -CH₃ stretching vibrations, -N₃ asymmetric stretching vibrations, –CH₃ in-plane bending vibrations, -N₃ symmetric stretching vibrations, and fingerprint region. In previous studies, the N–N asymmetrical stretching vibration for Cl₂BN₃, Br₂BN₃, Me₂BN₃, (C₆F₅)₂BN₃ polymer, and NaN₃ crystal were individually located at 2210–2219 [15], 2200–2215 [15], 2128 [7, 14], 2135–2209 cm⁻¹ [11, 12], and 2128–2151 cm⁻¹ [29] from experiments. Our calculated results are in accordance with those in crystal, which shows that the structures of N₃ groups in clusters and in crystal are identical. Moreover, the obtained result is similar to that found in the clusters (HClBN₃)_n (n = 1 – 6) (2217–2250 cm⁻¹) of DFT calculations [21].

Furthermore, compared with monomer, the N₃ asymmetric stretching vibration presents the blue-shifted phenomenon for clusters with n = 2 − 6. However, the N₃ symmetric stretching vibration and the –CH₃ stretching vibration show red-shifted trend. Meanwhile, in three characteristic regions of N₃ asymmetric, N₃ symmetric, and –CH₃ stretching vibration, the number of vibration mode equals to that of azido groups and C–H bonds, respectively. For example, the monomer 1 has three bands at 2923, 2972, and 3022 cm⁻¹ with C–H stretching vibration, and the trimer 3 has three bands at 2213, 2225, and 2240 cm⁻¹ with N₃ asymmetric stretching vibration, and the hexamer 6 has six bands at 1237, 1237, 1245, 1245, 1247, and 1255 cm⁻¹ with N₃ symmetric stretching vibration.

3.4. Thermodynamic Properties

Thermodynamic functions are important parameters for clusters to predict reactive property in a chemical reaction. According to vibrational analysis and statistical thermodynamic method, the standard molar heat capacity (), standard molar thermal entropy (), and standard molar thermal enthalpy () of the asymmetric clusters (CH₃FBN₃)_n (n = 1 – 6) in the range of 200–800 K are evaluated and tabulated in Table 4. It is obvious that the calculated thermodynamic functions increase with the temperature T raising. For more clear intuitive, taking monomer 1 as an example, the temperature-dependent relationships for , , and are expressed in formulas (2)–(4) and all are plotted in Figure 4(a). These correlations approximate to linear equations due to the small coefficients of T²; namely, the , , and increase linearly with the increase of temperature T. This can be understood from the fact that these three thermodynamic functions are dominated by the weak translational and rotational motions of the clusters at lower temperature, whereas the vibrational motion is intensified and makes more contributions to , , and at higher temperature. The same linear relationships are found for clusters (CH₃FBN₃)_n with n = 2 – 6:where R² represents the square of correlation coefficient and SD represents standard deviation.

(a)

(b)

Moreover, the cluster size-dependent relationships for , , and are expressed in formulas (5)–(7) and all are shown in Figure 4(b). All thermodynamic functions increase monotonically with the enlarged cluster size n; in other words, when one more CH₃FBN₃ is bound, the , , and increase with the average of 108 J·mol⁻¹ K⁻¹, 133 J·mol⁻¹ K⁻¹, and 18 kJ·mol⁻¹, separately. This means that the contribution of monomer CH₃FBN₃ to the thermodynamic properties of cluster matches the cluster additivity:

In addition, the theoretical enthalpies (ΔH) and Gibbs free energies (ΔG) of various oligomerizations from monomer CH₃FBN₃ in the range of 200–800 K are compiled in Table 5. The values of ΔH in the processes are negative except for the process 1 ⟶ 2 beyond 700 K, indicating that these oligomerization processes are exothermic. The ΔG at a given temperature is evaluated by the equation ΔG = ΔH − TΔS. The values of ΔG are all positive, which reveals the oligomerizations cannot occur spontaneously in the range of 200–800 K. There are no experimentally thermodynamic data available for the asymmetric clusters (CH₃FBN₃)_n (n = 1 − 6), so the calculated thermodynamic functions and the obtained relationships of them with the temperature and cluster size n may help the experiment to further study the physical, chemical, and energetic properties of the asymmetric clusters (CH₃FBN₃)_n (n = 1 − 6) or other asymmetric boron azides.

3.5. Aromatic Properties

Here, the aromaticity of the studied systems will be discussed. Because our systems are nonplanar, it is not suitable to use the criterion of nucleus-independent chemical shift (NICS) [30]. In order to find out whether a large π bond exists in our studied system, we use the newly proposed localized orbital locator (LOL)-π method [31] that can be used for studying nonplanar system to study the π bonds of our systems. The LOL-π is analyzed and visualized with the Multiwfn [32]. From Figure 5, there is π bond of NNNB in 1 and similar π bonds in 2-6. However, the π conjugation of 2–6 is not as good as that of 1. Meanwhile, Figure 5 also shows no large π bonds in all systems.

4. Conclusions

We have systematically studied the structure, relative stability, IR, and thermodynamic properties of the asymmetric clusters (CH₃FBN₃)_n (n = 1 – 6) at the DFT-B3LYP/6-31G. The B and N_α atoms tend to bond together in clusters (CH₃FBN₃)_n (n = 2 − 6). The variation trend of geometrical parameters shows N₂ (N_β−N_γ), -CH₃, and F^- groups are easily eliminated and BN material is yielded. The calculated Δ₂E of the asymmetric clusters (CH₃FBN3)n (n = 1 − 6) exhibits a pronounced odd-even alternation phenomenon with cluster size n increasing, indicating that the cluster at n = 3 is more stable than other clusters. From monomer (n = 1) to clusters (n = 2 – 6), the N₃ asymmetric stretching vibration presents blue-shifted trend while the N₃ symmetric stretching vibration and –CH₃ stretching vibration are red-shifted. The thermodynamic functions (, , and ) of clusters (CH₃FBN₃)_n (n = 1 – 6) show linear increase with the augment of both temperature T and cluster size n of clusters. Judged by the enthalpies in the range of 298.2–600 K, the calculated thermodynamic properties demonstrate that the formation of clusters (CH₃FBN₃)_n (n = 2 − 6) from the monomer is thermodynamically favorable; however, the formation cannot occur spontaneously.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Authors’ Contributions

Qi-Ying Xia conceptualized the study and was responsible for project administration; Deng-Xue Ma, Yao-Yao Wei, and Yun-Zhi Li were involved in data curation; Guo-Kui Liu was involved in resource management; Deng-Xue Ma and Yao-Yao Wei wrote the original draft; and Qi-Ying Xia and Guo-Kui Liu wrote and edited the manuscript. Deng-Xue Ma and Yao-Yao Wei contributed equally to the work.

Acknowledgments

This work was supported by the Natural Science Foundation of Shandong Province (grant no. ZR2017LB011) and the Undergraduate Education Reform Project of Shandong Province (grant no. Z2018S006).

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Copyright © 2020 Deng-Xue Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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